Abstract:Grid-following voltage source converter (GFL-VSC) and grid-forming voltage source converter (GFM-VSC) have different dynamic characteristics for active power-frequency and reactive power-voltage supports of the power grid. This paper aims to clarify and recognize the difference between grid-following (GFL) and grid-forming (GFM) frequency-voltage support more intuitively and clearly. Firstly, the phasor model considering circuit constraints is established based on the port circuit equations of the converter. It is revealed that the voltage and active power linearly correspond to the horizontal and vertical axes in the phasor space referenced to the grid voltage phasor. Secondly, based on topological homology, GFL and GFM controls are transformed and mapped into different trajectories. The topological similarity of the characteristic curves for GFL and GFM controls is the essential cause of their uniformity. Based on the above model, it is indicated that GFL-VSC and GFM-VSC possess uniformity with regard to active power response, type of coupling, and phasor trajectory. They differ in synchronization, power coupling mechanisms, dynamics, and active power-voltage operation domain in the quasi-steady state. Case studies are undertaken on GFL-VSC and GFM-VSC integrated into a four-machine two-area system. Simulation results verify that the dynamic uniformity and difference of GFL-VSC and GFM-VSC are intuitively and comprehensively revealed.

Abstract:With the increase of the renewable energy generator capacity, the requirements of the power system for grid-connected converters are evolve, which leads to diverse control schemes and increased complexity of systematic stability analysis. Although various frequency-domain models are developed to identify oscillation causes, the discrepancies between them are rarely studied. This study aims to clarify these discrepancies and provide circuit insights for stability analysis by using different frequency-domain models. This study emphasizes the limitations of assuming that the transfer function of the self-stable converter does not have right half-plane (RHP) poles. To ensure that the self-stable converters are represented by a frequency-domain model without RHP poles, the applicability of this model of grid-following (GFL) and grid-forming (GFM) converters is discussed. This study recommends that the GFM converters with ideal sources should be represented in parallel with the P / Q - θ / V admittance model rather than the V - I impedance model. Two cases are conducted to illustrate the rationality of the P / Q - θ / V admittance model. Additionally, a hybrid frequency-domain modeling framework and stability criteria are proposed for the power system with several GFL and GFM converters. The stability criteria eliminates the need to check the RHP pole numbers in the non-passive subsystem when applying the Nyquist stability criterion, thereby reducing the complexity of stability analysis. Simulations are carried out to validate the correctness of the frequency-domain model and the stability criteria.

Abstract:Oscillations caused by small-signal instability have been widely observed in AC grids with grid-following (GFL) and grid-forming (GFM) converters. The generalized short-circuit ratio is commonly used to assess the strength of GFL converters when integrated with weak AC systems at risk of oscillation. This paper provides the grid strength assessment method to evaluate the small-signal synchronization stability of GFL and GFM converters integrated systems. First, the admittance and impedance matrices of the GFL and GFM converters are analyzed to identify the frequency bands associated with negative damping in oscillation modes dominated by heterogeneous synchronization control. Secondly, based on the interaction rules between the short-circuit ratio and the different oscillation modes, an equivalent circuit is proposed to simplify the grid strength assessment through the topological transformation of the AC grid. The risk of sub-synchronization and low-frequency oscillations, influenced by GFL and GFM converters, is then reformulated as a semi-definite programming (SDP) model, incorporating the node admittance matrix and grid-connected device capacities. The effectiveness of the proposed method is demonstrated through a case analysis.

Abstract:The integration of converter-interfaced generators (CIGs) into power systems is rapidly replacing traditional synchronous machines. To ensure the security of power supply, modern power systems require the application of grid-forming technologies. This study presents a systematic small-signal analysis procedure to assess the synchronization stability of grid-forming virtual synchronous generators (VSGs) considering the power system characteristics. Specifically, this procedure offers guidance in tuning controller gains to enhance stability. It is applied to six different grid-forming VSGs and experimentally tested to validate the theoretical analysis. This study concludes with key findings and a discussion on the suitability of the analyzed grid-forming VSGs based on the power system characteristics.

Abstract:The increasing adoption of grid-forming converters (GFMCs) stems from their capacity to furnish voltage and frequency support for power grids. Nevertheless, GFMCs employing the current reference saturation limiting method often exhibit instability during various transient disturbances including grid voltage sags, frequency variations, and phase jumps. To address this problem, this paper proposes a virtual power angle synchronous (δ_v-SYN) control method. The fundamental of this method is to achieve synchronization with the grid using the virtual power angle δ_v instead of the active power. The transient stability characteristics of the proposed method are theoretically elucidated using a novel virtual power angle-power angle (δ_v-δ) model. The key benefit of the proposed method is its robustness to various grid strengths and diverse forms of transient disturbances, eliminating the requirement for fault identification or control switching. Moreover, it can offer grid-forming support to the grid during grid faults. Hardware-in-the-loop experimental results validate the theoretical analysis and the performance of the proposed method.

Abstract:With photovoltaic (PV) sources becoming more prevalent in the energy generation mix, transitioning grid-connected PV systems from grid-following (GFL) mode to grid-forming (GFM) mode becomes essential for offering self-synchronization and active support services. Although numerous GFM methods have been proposed, the potential of DC voltage control malfunction during the provision of the primary and inertia support in a GFM PV system remains insufficiently researched. To fill the gap, some main GFM methods have been integrated into PV systems featuring detailed DC source dynamics. We conduct a comparative analysis of their performance in active support and DC voltage regulation. AC GFM methods such as virtual synchronous machine (VSM) face a significant risk of DC voltage failure in situations like alterations in solar radiation, leading to PV system tripping and jeopardizing local system operation. In the case of DC GFM methods such as matching control (MC), the active support falls short due to the absence of an accurate and dispatchable droop response. To address the issue, a matching synchronous machine (MSM) control method is developed to provide dispatchable active support and enhance the DC voltage dynamics by integrating the MC and VSM control loops. The active support capability of the PV systems with the proposed method is quantified analytically and verified by numerical simulations and field tests.

Abstract:As the proportion of renewable energy sources continues to increase, the local damping contributions of sources in power system decrease, posing a challenge to the power system stability. Therefore, online tracking of the damping contributions of each source is crucial for the prevention of low-frequency oscillations. This paper proposes an online tracking method of local damping under ambient data. The proposed method is based on dissipation energy spectrum analysis (DESA) and the energy dissipation factor (EDF). First, the feasibility of using frequency-domain analysis for the dissipation energy of generator is analyzed. The frequency spectral function of dissipation energy of generator is then derived by integrating with Parseval’s theorem, and the EDF is defined. Second, the generator energy dissipation factor (GEDF) for the dominant oscillation mode frequency is established. The modal information of the dominant oscillation in the power system is obtained through DESA. The relationship between the frequency spectral function and eigenvalues is also established. Finally, an online tracking method of local damping is proposed based on DESA and GEDF. The effectiveness of the proposed method is validated through simulations on a four-machine 11-bus power system and an actual power system in Northwest China.

Abstract:External disturbances can induce torsional oscillation with weak damping in the shaft system of permanent magnet synchronous generators (PMSGs) based wind generation system, thereby inducing low-frequency oscillations. However, the influence of electromagnetic torque on the shaft system damping and corresponding parameter laws have been scarcely explored. We define the electrical damping coefficient as a quantitative measure for the influence of electromagnetic torque on the shaft system damping. The torsional oscillation damping characteristics of the shaft system under vector control are analyzed, and the transfer function for electromagnetic torque and speed is derived. Additionally, we elucidate the mechanism by which the electromagnetic torque influences the shaft system damping. Simultaneously, laws describing the influence of wind speed, system parameters, and control parameters on the torsional oscillation damping are analyzed. Accordingly, the optimal damping angle of the shaft system a torsional oscillation suppression strategy is proposed to compensate for with uncertainty in the parameters affecting damping. The studied system is modeled using MATLAB/Simulink, and the simulation results validate the effectiveness of the theoretical analysis and proposed torsional oscillation suppression strategy.

Abstract:The flexible interconnection of microgrids (MGs) adopting back-to-back converters (BTBCs) has emerged as a new development trend in the field of MGs. This approach enables larger-scale integration and higher utilization of distributed renewable energy sources (RESs). However,their stability characteristics are very different from single MG due to the control characteristics of flexible interconnection. Meanwhile, the uncertainty and stochastic dependence structures of RESs and loads create challenges for stability analysis and cooperative control. In this paper, a probabilistic small-signal stability assessment and cooperative control framework is proposed for interconnected MGs via BTBCs. First, a cooperative control architecture for MGs is constructed. Then, a small-signal model of interconnected MGs via BTBCs containing primary control and secondary control is developed. This model facilitates the analysis of the impacts of BTBCs and various control strategies on the system stability. Subsequently, Copula functions and polynomial chaos expansion (PCE) are combined to achieve the probabilistic small-signal stability assessment. On this basis, the parameters of the cooperative control are optimized, enhancing the robustness of interconnected MGs via BTBCs. Finally, a case of interconnected MGs via BTBCs are built in MATLAB/Simulink to verify the accuracy and effectiveness of the proposed framework.

Abstract:For doubly-fed induction generator (DFIG)-based wind farms connected to flexible DC transmission system, the oscillation suppression after fault clearance proves very difficult. Addressing this problem, this paper constructs the dynamic energy model of the interconnected system, reveals the mechanism of oscillation instability after fault clearance, and designs an oscillation suppression strategy. First, by considering the dynamic characteristics of the control links in grid-connected DFIG-based wind farms via voltage source converter based high-voltage direct current (VSC-HVDC) transmission system, the interconnected system is divided into several subsystems, and the energy model of each subsystem is constructed. Furthermore, the magnitudes and directions of different interaction energy items are quantitatively analyzed, so that the key control links that transmit and magnify the system energy can be identified. On this basis, the corresponding supplementary control links are designed to suppress the system oscillation. Finally, the accuracy and effectiveness of the proposed oscillation suppression strategy are verified by hardware-in-loop tests. The results prove that the d-axis subsystem of DFIG grid-side converter (GSC) current inner loop, phase-locked loop (PLL), and q-axis subsystem of VSC-HVDC voltage outer loop are the key links that induce the oscillation to occur, and the proposed strategy shows promising results in oscillation suppression.

Abstract:With the rapid integration of renewable energy, wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues. Existing methods are usually studied for local power systems with around one hundred nodes. However, for a large-scale power system with tens of thousands of nodes, the dimension of transfer function matrix or the order of characteristic equation is much higher. In this case, the existing methods such as eigenvalue analysis method and impedance-based method have difficulty in computation and are thus hard to utilize in practice. To fill this gap, this paper proposes a novel method named the smallest eigenvalues based logarithmic derivative (SELD) method. It obtains the dominant oscillation modes by the logarithmic derivative of the k-smallest eigenvalue curves of the sparse extended nodal admittance matrix (NAM). An oscillatory stability analysis tool is further developed based on this method. The effectiveness of the method and the tool is validated through a local power system as well as a large-scale power system.

Abstract:Realistic uncertainties of renewable energies and loads may possess complicated probability distributions and correlations, which are difficult to be characterized by standard probability density functions and hence challenge existing uncertainty propagation analysis (UPA) methods. Also, nonintrusive spectral representation (SR)-based UPA methods can only estimate system responses at each time point separately, which is time-consuming for analyzing power system dynamics. Thus, this paper proposes a generic multi-output SR (GMSR) method to effectively tackle the above limitations by developing the generic correlation transformation and multi-output structure. The effectiveness and superiority of GMSR in efficiency and accuracy are demonstrated by comparing it with existing SR methods.

Abstract:Under-frequency load shedding (UFLS) serves as the very last resort for preventing total blackouts and cascading events. Fluctuating operating conditions and weak resilience of the future grid require UFLS adapt to various operating conditions and non-envisioned faults. This paper develops a novel data-enabled Koopman-based load shedding (KLS) to achieve the optimal one-shot load shedding for power system frequency safety. The KLS yields a network that facilitates a coordinate transformation from the delay-embedded space to a new space, wherein the dynamics can be expressed in a linear manner. The network is specifically tailored to effectively track parameter variations in the dynamic model of the power system. Linear dynamics support the development of a real-time decided load shedding strategy, while parameter tracking enables the adaptability of the KLS to non-envisioned operating conditions and faults. To address approximation inaccuracies and the discrete nature of load shedding, a safety margin tuning scheme is integrated into the KLS framework, ensuring that the system frequency trajectory remains within the safety range. Simulation results show the adaptability, prediction capability, and control effect of the proposed KLS.

Abstract:In DC power systems dominated by power electronic devices, constant power loads (CPLs) and saturation components significantly impact large-signal stability. During the large-signal stability analysis process, the presence of multiple state variables and high-order system poses substantial challenges. To address this, considering the complete control dynamics, this paper proposes an equivalent single-machine (ESM) model of the droop-based DC power systems to reduce the complexity of the large-signal analysis. Building on the proposed ESM model, considering the dynamics of CPL and saturation constraints, a region of attraction (ROA) estimation algorithm based on sum of squares (SOS) programming is proposed, which significantly reduces the conservativeness compared with other existing methods. Furthermore, a control parameter optimization algorithm based on SOS programming is proposed with the aim of expanding the ROA. Furthermgre, with the aim of expanding the ROA, controller sythesis is conducted with proposed control parameter optimization algorithm based on SOS programming. Ultimately, simulation experiments validate the accuracy of the proposed ESM model and the proposed ROA estimation algorithm, as well as the effectiveness of the control parameter optimization algorithm.

Abstract:In this paper, a set of distributed secondary controllers is introduced that provide active regulation for both steady-state and transient-state performances of an islanded DC microgrid (MG). The secondary control for distributed converter interfaced generation (DCIG) not only guarantees that the system converges to the desired operating states in the steady state but also regulates the state variations to a prescribed transient-state performance. Compared with state-of-the-art techniques of distributed secondary control, this paper achieves accurate steady-state secondary regulations with prescribed transient-state performance in an islanded DC MG. Moreover, the applicability of the proposed control does not rely on any explicit knowledge of the system topology or physical parameters. Detailed controller designs are provided, and the system under control is proved to be Lyapunov stable using large-signal stability analysis. The steady-state and transient-state performances of the system are analyzed. The paper proves that as the perturbed system converges, the proposed control achieves accurate proportional power sharing and average voltage regulation among the DCIGs, and the transient variations of the operating voltages and power outputs at each DCIG are regulated to the prescribed transient-state performance. The effectiveness of the proposed control is validated via a four-DCIG MG system.

Abstract:The virtual synchronous generator (VSG), utilized as a control strategy for grid-forming inverters, is an effective method of providing inertia and voltage support to the grid. However, the VSG exhibits limited capabilities in low-voltage ride-through (LVRT) mode. Specifically，the slow response of the power loop poses challenges for VSG in grid voltage support and increases the risk of overcurrent, potentially violating present grid codes. This paper reveals the mechanism behind the delayed response speed of VSG control during the grid faults. On this basis, a compound compensation control strategy is proposed for improving the LVRT capability of the VSG, which incorporates adaptive frequency feedforward compensation (AFFC), direct power angle compensation (DPAC), internal potential compensation (IPC), and transient virtual impedance (TVI), effectively expediting the response speed and reducing transient current. Furthermore, the proposed control strategy ensures that the VSG operates smoothly back to its normal control state following the restoration from the grid faults. Subsequently, a large-signal model is developed to facilitate parameter design and stability analysis, which incorporates grid codes and TVI. Finally, the small-signal stability analysis and simulation and experimental results prove the correctness of the theoretical analysis and the effectiveness of the proposed control strategy.

Abstract:The maximum power transfer capability (MPTC) of phase-locked loop (PLL)-based grid-following inverters is often limited under weak-grid conditions due to passivity violations caused by operating-point-dependent control loops. This paper reveals and compares the mechanisms of these violations across different control strategies. Using admittance decomposition and full-order state-space models for eigenvalue analysis, MPTC limitations from control loops and their interactions are identified. The small-signal stabilities of different control loops are compared under varying grid strength, and both static and dynamic MPTCs for each control mode are examined. This paper also explores how control loop interactions impact the MPTC, offering insights for tuning control loops to enhance stability in weak grids. For example, fast power control improves the MPTC when paired with a slow PLL, while power control has minimal effect when the PLL is sufficiently fast. The findings are validated through frequency scanning, eigenvalue analysis, simulations, and experiments.

Abstract:Fractional-order control (FOC) has gained significant attention in power system applications due to their ability to enhance performance and increase stability margins. In grid-connected converter (GCC) systems, the synchronous reference frame phase-locked loop (SRF-PLL) plays a critical role in grid synchronization for renewable power generation. However, there is a notable research gap regarding the application of FOC to the SRF-PLL. This paper proposes a fractional-order SRF-PLL (FO-SRF-PLL) that incorporates FOC to accurately track the phase angle of the terminal voltage, thereby improving the efficiency of grid-connected control. The dynamic performance of the proposed FO-SRF-PLL is evaluated under varying grid conditions. A comprehensive analysis of the small-signal stability of the GCC system employing the FO-SRF-PLL is also presented, including derived small-signal stability conditions. The results demonstrate that the FO-SRF-PLL significantly enhances robustness against disturbances compared with the conventional SRF-PLL. Furthermore, the GCC system with the FO-SRF-PLL maintains stability even under weak grid conditions, showing superior stability performance over the SRF-PLL. Finally, both simulation and experimental results are provided to validate the analysis and conclusions presented in this paper.

Abstract:The significant increase in the proportion of renewable energy sources (RESs) has elevated risks of extreme ramp events and frequency instability in power systems. In recent years, frequency stability events have occurred in several countries/regions worldwide due to flexibility deficiencies. Generation flexibility has emerged as a critical factor influencing the frequency stability of power systems. This paper proposes a domain of attraction (DOA)-based quantitative method to assess the frequency stability region of power systems with a high proportion of RESs, considering generation flexibility constraints. First, ramp rate is adopted as the core indicator to characterize generation flexibility within automatic generation control (AGC) timescale, through which a nonlinear AGC model with rate saturation constraints is established. Second, the concept of DOA is introduced to define the stability region of the nonlinear AGC. Third, a quadratic Lyapunov-based estimation method is employed to quantitatively analyze the DOA of the nonlinear AGC at different generation flexibility levels. Simulation results demonstrate that increased generation flexibility expands the estimated DOA of the nonlinear AGC, whereas generation flexibility deficiency induces AGC instability. Moreover, state trajectory and time-domain simulation verify that the proposed estimation method accurately represents the stability region of the nonlinear AGC.

Abstract:The integrated electricity-heat-hydrogen system (IEHHS) facilitates the efficient utilization of multiple energy sources, while the operational flexibility of IEHHS is hindered by the high heat inertia of alkaline electrolyzers (AELs) and the variations of renewable energy. In this paper, we propose a robust scheduling of IEHHS considering the bidirectional heat exchange (BHE) between AELs and district heating networks (DHNs). First, we propose an IEHHS model to coordinate the operations of AELs, active distribution networks (ADNs), and DHNs. In particular, we propose a BHE that not only enables the waste heat recovery for district heating but also accelerates the thermal dynamics in AELs. Then, we formulate a two-stage robust optimization (RO) problem for the IEHHS operation to consider the variability of renewable energy in ADNs. We propose a new solution method, i.e., multi-affine decision rule (MADR), to solve the two-stage RO problem with less conservatism. The simulation results show that the operational flexibility of IEHHS with BHE is remarkably improved compared with that only with unidirectional heat exchange (UHE). Compared with the traditional affine decision rule (ADR), the MADR effectively reduces the IEHHS operating costs while guaranteeing the reliability of scheduling strategies.

Abstract:The increasing integration of renewable energy sources poses great challenges to the power system frequency security. However, the existing electricity market mechanism lacks integration and incentives for emerging frequency regulation (FR) resources such as wind power generators (WPGs), which may reduce their motivation to provide frequency support and further deteriorate the frequency dynamics. In this paper, a market scheduling and pricing method for comprehensive frequency regulation services (FRSs) is proposed. First, a modeling approach for flexible FR capabilities of WPGs is proposed based on the mechanism of inertia control and power reserve control. Subsequently, considering the differences in inverter control strategies, a novel system frequency response model with grid-following and grid-forming inverters is established. Combined with the automatic generation control, the frequency security constraints of the whole FR process are derived, and integrated into the market scheduling model to co-optimize the energy and FRSs. Finally, by distinguishing the contributions of various types of resources in different FR stages, a differentiated pricing scheme is proposed to incentivize producers with various regulation qualities to provide FRSs. The effectiveness of the proposed method is verified on the modified IEEE 6-bus system and the IEEE RTS-79 system.

Abstract:This paper develops a detailed equivalent model for modular multilevel converters with partially-integrated battery energy storage. The proposed model gains computational efficiency in two ways. Firstly, it markedly reduces the large number of nodes in the conventional switching model of the converter, thereby shrinking the size of its admittance matrix. Secondly, it avoids computationally expensive re-triangularization of the admittance matrix during the normal operation of the converter and restricts it only to the rare occasions of converter blocking. Mathematical derivation of the model is carried out using differential equations of the converter. The computational efficiency and accuracy of the proposed model are confirmed by comparison of the results from its implementation in the PSCAD/EMTDC simulator against conventional detailed switching models and measurements from a single-phase scaled-down laboratory setup. This paper also shows a case study wherein a converter with partially-integrated batteries is included in the CIGRE B4-5 benchmark system.

Abstract:The self-synchronizing voltage source inverter (SSVSI) is widely studied because of its grid-forming capability. However, the slow response of the active power control loop (APCL) under the weak grid makes it difficult for the SSVSI to quickly support the frequency of a low-inertia grid. In this paper, a grid framework is established to analyze the frequency support service process of the SSVSI, and the shortcomings of the regulation of the damping coefficient and virtual inertia coefficient for frequency support are analyzed. Then, an adaptive additional damping control method is proposed to optimize the ability of SSVSI to support the grid frequency. The proposed control method adjusts the damping of the APCL without affecting the system steady-state characteristics, which improves the active power response speed of the SSVSI. Besides, the proposed control method adaptively adjusts the additional damping coefficient based on the active power response without measuring the grid parameters. Compared with other forms of control, the proposed control method excels in minimizing the rate of change of frequency (RoCoF) and the frequency deviation (FD) within the grid, without succumbing to the constraints posed by unknown grid parameters. Furthermore, the analysis of the system stability is also presented. Finally, the experimental hardware results obtained from a miniaturized grid prototype are presented, corroborating the effectiveness of the proposed control method.

Abstract:Planning the low-carbon transition pathway of the power sector to meet the carbon neutrality goal poses a significant challenge due to the complex interplay of temporal, spatial, and cross-domain factors. A novel framework is proposed, grounded in the cyber-physical-social system in energy (CPSSE) and whole-reductionism thinking (WRT), incorporating a tailored mathematical model and optimization method to formalize the co-optimization of carbon reduction and carbon sequestration in the power sector. Using the carbon peaking and carbon neutrality transition of China as a case study, clustering method is employed to construct a diverse set of strategically distinct carbon trajectories. For each trajectory, the evolution of the generation mix and the deployment pathways of carbon capture and storage (CCS) technologies are analyzed, identifying the optimal transition pathway based on the criterion of minimizing cumulative economic costs. Further, by comparing non-fossil energy substitution and CCS retrofitting in thermal power, the analysis highlights the potential for co-optimization of carbon reduction and carbon sequestration. The results demonstrate that leveraging the spatiotemporal complementarities between the two can substantially lower the economic cost of achieving carbon neutrality, providing insights for integrated decarbonization strategies in power system planning.

Abstract:Transmission expansion planning (TEP) addresses the intricate task of optimizing new transmission infrastructure within an existing grid to meet system objectives. As a critical strategy in power system development, TEP significantly influences the long-term efficiency, reliability, and scalability of the network, with enduring effects on overall system performance. This paper explores the application of unconventional high surge impedance loading (HSIL) lines as a cost-effective alternative to conventional extra high-voltage (EHV) transmission lines. By optimizing the geometry of subconductors, HSIL designs could achieve higher power delivery capacities while operating at reduced voltage levels, addressing the increased demand for sustainable energy infrastructure. Two 500 kV HSIL line configurations are analyzed for their feasibility in replacing the conventional 765 kV transmission lines for the TEP to integrate the large-scale wind energy sources located in far remote areas. The analysis is carried out within the 23-bus EHV test system. This study reveals that both HSIL line configurations successfully meet the technical constraints of the TEP problem, ensuring reliable system operation even under contingency conditions. Therefore, the HSIL lines offer significant cost savings due to infrastructure and accessories at reduced voltage levels with much smaller right of way (ROW) than conventional counterparts. This underscores the potential of unconventional HSIL lines to contribute to more sustainable and cost-effective grid planning strategies for integrating large-scale renewable energy sources.

Abstract:The utilization of high-voltage direct current (HVDC) lines for the segmentation of the European power grid has been demonstrated to be a highly effective strategy for the mitigation of the risk of cascading blackouts. In this study, an accurate and efficient method for determining the optimal power flow through HVDC lines is presented, with the objective of minimizing load shedding. The proposed method is applied to two distinct scenarios: first, the segmentation of the power grid along the Pyrenees, with the objective of segmenting the Iberian Peninsula from the rest of Europe; and second, the segmentation of the power grid into Eastern and Western Europe, approximately in half. In both scenarios, the method effectively reduces the size of blackouts impacting both sides of the HVDC lines, resulting in a 46% and 67% reduction in total blackout risk, respectively. Furthermore, we have estimated the cost savings from risk reduction and the expenses associated with converting conventional lines to HVDC lines. Our findings indicate that segmenting the European power grid with HVDC lines is economically viable, particularly for segmenting the Iberian Peninsula, due to its favorable cost-risk reduction ratio.

Abstract:The widespread penetration of wind power has introduced challenges in managing the rotor angle stability characteristics of the power system, affecting both small- and large-disturbance rotor angle stabilities due to its uncertain steady-state power output and inverter-based grid interfacing. Traditionally, the two stability criteria are separately analyzed and improved via preventive control, e.g., generation rescheduling. However, they may have conflicting relationship during the preventive control optimization. Therefore, this paper firstly integrates both small- and large-disturbance rotor angle stabilities and proposes an optimization model for preventive generation rescheduling to simultaneously improve them while considering wind power uncertainty. The stability constraints are linearized using trajectory sensitivity analysis, while the wind power fluctuation is represented by employing a scenario-based Taguchi’s orthogonal array testing (TOAT) method. An iterative solution method is proposed to efficiently solve the optimization model. The proposed optimization model is established on the New England 10-machine 39-bus system and a large Nordic system, demonstrating its robustness and effectiveness in addressing wind power fluctuations.

Abstract:The mutual impedance between doubly-fed induction generator (DFIG) system and weak grid may cause a resonance, which yields to undesirable distortions and harmonics. The equivalent impedance of DFIG systems is high, which creates high-frequency resonance (HFR) in interaction with weak grids. Although several studies are conducted to mitigate HFRs, more improvements are needed in terms of damping and phase-margin. Accordingly, an active damping control strategy based on virtual admittance is proposed, which properly mitigates the disturbances. The proposed strategy is accurate as it considers the dynamic high-frequency model of DFIG system to effectively reduce the HFR. The performance of the proposed strategy is verified by using different case studies on a 2 MW DFIG system with time-domain simulations in MATLAB/Simulink environment.

Abstract:This paper proposes a novel control scheme for inverter-based resources (IBRs) based on the complex frequency (CF) concept. The control objective is to maintain a constant CF of voltage at the terminals of IBR by adjusting its current reference. This current is imposed based on the well-known power flow equation, the dynamics of which are calculated through estimating the CFs for the voltages of adjacent buses. The performance is evaluated by analyzing the local variations in frequency and voltage magnitude, as well as the frequency of center of inertia (CoI), and then compared with conventional frequency droop, proportional-integral (PI) voltage controllers, and virtual inertia. The case study utilizes a modified version of WSCC 9-bus system and a 1479-bus model of the Irish transmission grid and considers various contingencies and sensitivities such as the impact of current limiters, delays, noise, R/X ratio, and electromagnetic transient (EMT) dynamics. Results show that the proposed control scheme consistently outperforms the conventional controllers, leading to significant improvements in the overall dynamic response of the system.

Abstract:The data-driven approaches have been extensively developed for multi-operation impedance modeling of the renewable power generation equipment (RPGE). However, due to the black box of RPGE, the dataset used for establishing impedance model lacks theoretical guidance for data generation, which reduces data quality and results in a large amount of data redundancy. To address this issue, this paper proposes an impedance dataset optimization method for data-driven modeling of RPGE considering multi-operation conditions. The objective is to improve the data quality of the impedance dataset, thereby reflecting the overall impedance characteristics with a reduced data amount. Firstly, the impact of operation conditions on impedance is evaluated to optimize the selection of operating points. Secondly, at each operating point, the frequency distribution is designed to reveal the impedance characteristics with fewer measurement points. Finally, a serial update method for measured datasets and the multi-operation impedance model is developed to further refine the dataset. The experiments based on control-hardware-in-loop (CHIL) are conducted to verify the effectiveness of the proposed method.

Abstract:As the scale of power system continues to grow, a fast and accurate distributed optimal power flow solver becomes crucial for the effective dispatch of power system. This paper presents a learning to optimize (L2O) approach to accelerating the distributed optimal power flow solving. The final convergence values of global variables and Lagrange multipliers of the alternating direction method of multipliers (ADMM) are estimated as its warm-start solution. A long short-term memory-variational auto-encoder (LSTM-VAE) model is developed as the core for estimating the convergence value, and the LSTM-VAE assisted ADMM is proposed. The LSTM generates low-dimensional representations of global variables and Lagrange multipliers, while the decoder part of VAE reconstructs the high-dimensional asymptotic convergence values. A novel loss function is designed in the form of a quadratic sum penalty term to incorporate the constraint violations of the Lagrange multipliers. Additionally, a two-stage training data generation strategy is proposed to efficiently generate substantial data within a limited amount of time. The effectiveness of the LSTM-VAE assisted ADMM is evaluated using the modified IEEE 123-bus system, a synthetic 500-bus system, and a 793-bus system.

Abstract:Optimal capacity configuration (OCC) of large-scale energy bases with multi-timescale operation characteristics presents a critical challenge. To address the problem, this study proposes an OCC approach of large-scale energy bases considering external multi-stochastic scenarios and interactive multi-timescale objectives. Firstly, guided by the system theory, the nonlinear state-space description is presented for systematic analysis of a general large-scale energy base. Due to interactive multi-timescale objectives between annual and daily cumulative objectives, a nested optimization structure is established. Then, considering the external multi-stochastic scenarios caused by the variables such as wind speed, solar irradiance, electric load, and thermal load, a multi-step optimization strategy is proposed including pre-configuration in regular scenarios and re-configuration by introducing micro-incremental scenarios. The multi-step optimization strategy and nested optimization structure jointly achieve the OCC of the large-scale energy base. In each step, the nested optimization structure is executed once. Finally, while ensuring the balance between thermal supply and load demand, the imbalances between electric power supply and the load demand are eliminated, significantly showing the efficiency of the proposed OCC approach.

Abstract:This paper introduces a machine learning (ML) based model predictive control (MPC) with piecewise-affine approximation (PWA) structure for maximizing wind energy capture for an individual wind turbine operating in wind farms with low-quality wind resources. While MPC has the capability to systematically consider the stochasticity of wind speed and the dynamic process of wind turbine, its real-time implementation in a hardware controller of wind turbine has not been successful due to its high online computational burden and stringent execution time requirement in practice. To address this long-standing issue, this paper proposes a two-phase ML-based method consisting of linear regression and clustering to construct a PWA of the optimal law for original MPC scheme. The two-phase ML-based method is tunable with computational complexity, which can be adjusted to meet the hardware limitation of the given controller of wind turbine to enable real-time implementation, while preserving the optimality of linearized full-fidelity MPC as much as possible. We conduct simulations and experiments to demonstrate the effectiveness of the two-phase ML-based method.

Abstract:With the increasing number of distributed flexible resources with energy storage capabilities in virtual power plants (VPPs), the traditional market clearing model that only includes quantity and price bids cannot fully unlock their potential flexibility. In light of this, we propose a market clearing model for energy-constrained virtual power plants (EC-VPPs) based on distributionally robust chance-constrained optimization (DRCCO) with moment information. Furthermore, to address the uncertainty of EC-VPPs in the electricity market, a pricing strategy for EC-VPPs is proposed. This strategy helps quantify the impact of uncertainty in EC-VPPs on the system economy. The proposed market clearing model is reformulated as a tractable mixed-integer second-order cone programming (MISOCP) problem via a two-sided distributionally robust chance-constrained convex reformulation method. Numerical simulations verify that the proposed pricing strategy offers fair incentives for both reserve providers and uncertain sources, and delivers an effective market mechanism for the EC-VPPs.

Abstract:High proportion of renewable energies and the installation of power electronic devices (PEDs) pose tough challenges to the operation of power systems. In this paper, the remote coordination adjustment (RCA) of PEDs in stochastic scenarios is studied. The steady-state model for the AC/DC system with PEDs is first established, and the alternate iteration method based on linearization (AIML) is adopted, especially for efficient deterministic power flow calculation. Then, the RCA is proposed using a modular local sensitivity method combined with AIML, which can adjust the electrical variables by diverse PEDs with high efficiency. Additionally, the probabilistic power flow calculation using the quasi-Monte Carlo method with the adaptive sampling number (ASN-QMC) is introduced to keep the balance between the computational efficiency and accuracy, as well as demonstrating the positive impact of RCA by the PEDs in stochastic scenarios. The effectiveness of the proposed RCA is validated by a series of modified IEEE test systems.

Abstract:The subsynchronous oscillations (SSOs) related to renewable generation seriously affect the stability and safety of the power systems. To realize the dynamic monitoring of SSOs by utilizing the high computational efficiency and noise-resilient features of the matrix pencil method (MPM), this paper proposes an improved MPM-based parameter identification with synchrophasors. The MPM is enhanced by the angular frequency fitting equations based on the characteristic polynomial coefficients of the matrix pencil to ensure the accuracy of the identified parameters, since the existing eigenvalue solution of the MPM ignores the angular frequency conjugation constraints of the two fundamental modes and two oscillation modes. Then, the identification and recovery of bad data are proposed by utilizing the difference in temporal continuity of the synchrophasors before and after noise reduction. The proposed parameter identification is verified with synthetic, simulated, and actual measured phase measurement unit (PMU) data. Compared with the existing MPM, the improved MPM achieves better accuracy for parameter identification of each component in SSOs, better real-time performance, and significantly reduces the effect of bad data.

Abstract:This paper proposes an empirical wavelet transform (EWT) based method for identification and analysis of sub-synchronous oscillation (SSO) modes in the power system using phasor measurement unit (PMU) data. The phasors from PMUs are preprocessed to check for the presence of oscillations. If the presence is established, the signal is decomposed using EWT and the parameters of the mono-components are estimated through Yoshida algorithm. The superiority of the proposed method is tested using test signals with known parameters and simulated using actual SSO signals from the Hami Power Grid in Northwest China. Results show the effectiveness of the proposed EWT-Yoshida method in detecting the SSO and estimating its parameters.

Abstract:Due to the fact that a high share of renewable energy sources (RESs) are connected to high-voltage direct current (HVDC) sending-end AC power systems, the voltage and frequency regulation capabilities of HVDC sending-end AC power systems have diminished. This has resulted in potential system operating problems such as overvoltage and overfrequency, which occur simultaneously when block faults exist in the HVDC link. In this study, a steady-state voltage security-constrained optimal frequency control method for weak HVDC sending-end AC power systems is proposed. The integrated virtual inertia control of RESs is employed for system frequency regulation. Additional dynamic reactive power compensation devices are utilized to control the voltage of all nodes meet voltage security constraints. Then, an optimization model that simultaneously considers the frequency and steady-state voltage security constraints for weak HVDC sending-end AC power systems is established. The optimal control scheme with the minimum total cost of generation tripping and additional dynamic reactive power compensation required is obtained through the optimization solution. Simulations are conducted on a modified IEEE 9-bus test system and practical Qing-Yu line commutated converter based HVDC (LCC-HVDC) sending-end AC power system to verify the effectiveness of the proposed method.

Abstract:A day-ahead voltage-stability-constrained network topology optimization (DVNTO) problem is proposed to find the day-ahead topology schemes with the minimum number of operations (including line switching and bus-bar splitting) while ensuring the sufficient hourly voltage stability margin and the engineering operation requirement of power systems. The AC continuation power flow and the uncertainty from both renewable energy sources and loads are incorporated into the formulation. The proposed DVNTO problem is a stochastic, large-scale, nonlinear integer programming problem. To solve it tractably, a tailored three-stage solution methodology, including a scenario generation and reduction stage, a dynamic period partition stage, and a topology identification stage, is presented. First, to address the challenges posed by uncertainties, a novel problem-specified scenario reduction process is proposed to obtain the representative scenarios. Then, to obtain the minimum number of necessary operations to alter the network topologies for the next 24-hour horizon, a dynamic period partition strategy is presented to partition the hours into several periods according to the hourly voltage information based on the voltage stability problem. Finally, a topology identification stage is performed to identify the final network topology scheme. The effectiveness and robustness of the proposed three-stage solution methodology under different loading conditions and the effectiveness of the proposed partition strategy are evaluated on the IEEE 118-bus and 3120-bus power systems.

Abstract:This letter studies large-disturbance stability of the power system with a synchronous generator (SG) and a converter-interfaced generation (CIG) connected to infinite bus. The power system is multi-timescale and first simplified. It is shown that the boundary of region of attraction (ROA) of the simplified model is composed of stable manifolds of unstable equilibrium point (UEP) or semi-singular point (SSP), named anchor points, and singular surface pieces. The type of anchor point determines the dominant instability pattern of the power system. When the anchor point is UEP or SSP, the dominant instability pattern is the instability of rotor angle of SG or the instability of phase-locked loop and outer control loop (OCL) of CIG, respectively. Transition of dominant instability pattern can be analyzed with the relative position relationship between UEP and SSP. The effect of OCL is discussed. When the OCL is activated, the ROA becomes smaller and the system is more prone to instability of CIG. It is necessary to consider the OCL when studying the large-disturbance stability of the power system.

Abstract:To tackle emerging power system small-signal stability problems such as wideband oscillations induced by the large-scale integration of renewable energy and power electronics, it is crucial to review and compare existing small-signal stability analysis methods. On this basis, guidance can be provided on determining suitable analysis methods to solve relevant small-signal stability problems in power electronics-dominated power systems (PEDPSs). Various mature methods have been developed to analyze the small-signal stability of PEDPSs, including eigenvalue-based methods, Routh stability criterion, Nyquist/Bode plot based methods, passivity-based methods, positive-net-damping method, lumped impedance-based methods, bifurcation-based methods, etc. In this paper, the application conditions, advantages, and limitations of these criteria in identifying oscillation frequencies and stability margins are reviewed and compared to reveal and explain connections and discrepancies among them. Especially, efforts are devoted to mathematically proving the equivalence between these small-signal stability criteria. Finally, the performance of these criteria is demonstrated and compared in a 4-machine 2-area power system with a wind farm and an IEEE 39-bus power system with 3 wind farms.

Abstract:Renewable energy sources (RESs) are rapidly developing and their substitution for traditional power generation poses significant challenges to the frequency regulation in power systems. The load damping factor D characterizes the active power of load that changes with power system frequency, which is an important factor influencing the frequency response. However, the value of D is small, resulting in the limitation in frequency regulation of the power system. This paper proposes a parallel-type load damping factor controller to enhance load damping factor by utilizing static var generators (SVGs) in substations. Additionally, it discusses the configuration method for the relevant parameters of the controller, evaluates its frequency regulation capability, investigates the impact of large-scale application of the controller on static and dynamic loads, and conducts a comprehensive evaluation of the impact of the damping factor control process on the voltage stability of the main grid. The large-scale application of the proposed controller can significantly improve the frequency regulation capability, and almost have no influence on the working status of the load. It can also significantly improve the dynamic performance of system frequency. The proposed controller can provide technical support for the frequency regulation of new power systems with high proportion of RESs.

Abstract:In recent years, with increasing amounts of renewable energy sources connecting to power networks, sub-/super-synchronous oscillations (SSOs) have occurred more frequently. Due to the time-variant nature of SSO magnitudes and frequencies, as well as the mutual interferences among SSO modes with close frequencies, the accurate parameter estimation of SSO has become a particularly challenging topic. To solve this issue, this paper proposes an improved spectrum analysis method by improving the window function and a spectrum correction method to achieve higher precision. First, by aiming at the sidelobe characteristics of the window function as evaluation criteria, a combined cosine function is optimized using a genetic algorithm (GA). Furthermore, the obtained window function is self-convolved to extend its excellent characteristics, which have better performance in reducing mutual interference from other SSO modes. Subsequently, a new form of interpolated all-phase fast Fourier transform (IpApFFT) using the optimized window function is proposed to estimate the parameters of SSO. This method allows for phase-unbiased estimation while maintaining algorithmic simplicity and expedience. The performance of the proposed method is demonstrated under various conditions, compared with other estimation methods. Simulation results validate the effectiveness and superiority of the proposed method.

Abstract:In the existing small-signal stability constrained optimal power flow (SSSC-OPF) algorithms, only the rightmost eigenvalue or eigenvalues that do not satisfy a given threshold, e.g., damping ratio threshold and real-part threshold of eigenvalue, are considered in the small-signal stability constraints. The effect of steady-state, i.e., operating point, changes on eigenvalues is not fully taken into account. In this paper, the small-signal stability constraint that can fully reflect the eigenvalue change and system dynamic performance requirement is formed by analyzing the eigenvalue distribution on the complex plane. The small-signal stability constraint is embedded into the standard optimal power flow model for generation rescheduling. The simultaneous solution formula of the SSSC-OPF is established and solved by the quasi-Newton approach, while penalty factors corresponding to the eigenvalue constraints are determined by the stabilization degree of constrained eigenvalues. To improve the computation speed, a hybrid algorithm for eigenvalue computation in the optimization process is proposed, which includes variable selection for eigenvalue estimation and strategy selection for eigenvalue computation. The effectiveness of the proposed algorithm is tested and validated on the New England 10-machine 39-bus system and a modified practical 68-machine 2395-bus system.

Abstract:Since the scale and uncertainty of the power system have been rapidly increasing, the computation efficiency of constructing the security region boundary (SRB) has become a prominent problem. Based on the topological features of historical operation data, a sample generation method for SRB identification is proposed to generate evenly distributed samples, which cover dominant security modes. The boundary sample pair (BSP) composed of a secure sample and an unsecure sample is defined to describe the feature of SRB. The resolution, sampling, and span indices are designed to evaluate the coverage degree of existing BSPs on the SRB and generate samples closer to the SRB. Based on the feature of flat distribution of BSPs over the SRB, the principal component analysis (PCA) is adopted to calculate the tangent vectors and normal vectors of SRB. Then, the sample distribution can be expanded along the tangent vector and corrected along the normal vector to cover different security modes. Finally, a sample set is randomly generated based on the IEEE standard example and another new sample set is generated by the proposed method. The results indicate that the new sample set is closer to the SRB and covers different security modes with a small calculation time cost.

Abstract:With the rapid increase in the installed capacity of renewable energy in modern power systems, the stable operation of power systems with considerable power electronic equipment requires further investigation. In converter-based islanded microgrid (CIM) systems equipped with grid-following (GFL) and grid-forming (GFM) voltage-source converters (VSCs), it is challenging to maintain stability due to the mutual coupling effects between different VSCs and the loss of voltage and frequency support from the power system. In previous studies, quantitative transient stability analysis was primarily used to assess the active power loop of GFM-VSCs. However, frequency and voltage dynamics are found to be strongly coupled, which strongly affects the estimation result of stability boundary. In addition, the varying damping terms have not been fully captured. To bridge these gaps, this paper investigates the transient stability of CIM considering reactive power loop dynamics and varying damping. First, an accuracy-enhanced nonlinear model of the CIM is derived based on the effects of reactive power loop and post-disturbance frequency jump phenomena. Considering these effects will eliminates the risk of misjudgment. The reactive power loop dynamics make the model coefficients be no longer constant and thus vary with the power angle. To evaluate quantitatively the effects of reactive power loop and varying damping on the transient stability of CIM, an iterative criterion based on the equal area criterion theory is proposed. In addition, the effects of parameters on the stable boundary of power system are analyzed, and the dynamic interaction mechanisms are revealed. Simulation and experiment results verify the merits of the proposed method.

Abstract:High-precision synchronized measurement data with short measurement latency are required for applications of phasor measurement units (PMUs). This paper proposes a synchrophasor measurement method based on cascaded infinite impulse response (IIR) and dual finite impulse response (FIR) filters, meeting the M-class and P-class requirements in the IEC/IEEE 60255-118-1 standard. A low-group-delay IIR filter is designed to remove out-of-band interference components. Two FIR filters with different center frequencies are designed to filter out the fundamental negative frequency component and obtain synchrophasor estimates. The ratio of the amplitudes of the synchrophasor is used to calculate the frequency according to the one-to-one correspondence between the ratio of the amplitude frequency response of the FIR filters and the frequency. To shorten the response time introduced by IIR filter, a step identification and processing method based on the rate of change of frequency (RoCoF) is proposed and analyzed. The synchrophasor is accurately compensated based on the frequency and the frequency response of the IIR and FIR filters, achieving high-precision synchrophasor and frequency estimates with short measurement latency. Simulation and experiment tests demonstrate that the proposed method is superior to existing methods and can provide synchronized measurement data for M-class PMU applications with short measurement latency.

Abstract:Droop-based fast frequency response (FFR) control of wind turbines can improve the frequency performance of power systems with high penetration of wind power. Explicitly formulating the feasible region of the droop-based FFR controller parameters can allow system operators to conveniently assess the feasibility of FFR controller parameter settings to comply with system frequency security, and efficiently tune and optimize FFR controller parameters to meet frequency security requirements. However, the feasible region of FFR controller parameters is inherently nonlinear and implicit because the power point tracking controllers of wind turbine would counteract the effect of FFR controllers. To address this issue, this letter proposes a linear feasible region formulation method, where frequency regulation characteristics of wind turbines, the dead band, and reserve limits of generators are all considered. The effectiveness of the proposed method and its application is demonstrated on a 10-machine power system.

Abstract:During the power modulation process of line commutated converter-based high-voltage direct current (LCC-HVDC), the transient power mismatch between the fast-change converter station and the slow-response reactive power compensators (RPCs) can cause transient voltage disturbances at the weak sending end of the AC grid. To mitigate such voltage disturbances, this paper proposes a coordinated feedback power control method for the hybrid multi-infeed HVDC (HMI-HVDC) system comprising an LCC-HVDC and voltage source converter-based HVDC (VSC-HVDC) systems. The mechanism of the disturbance caused by transient power mismatch is quantitatively analyzed, and the numerical relationship between the instantaneous unbalanced power and the AC voltage is derived. Based on the numerical relationship and considering the time-varying relationship of reactive power between converter stations, the unbalanced power is set as the feedback and coordinately distributed among the inverter stations of VSC-HVDC, and the rectifier and the inverter stations of LCC-HVDC. Simulation results verify that the proposed method can effectively suppress voltage disturbance without relying on remote communication, thus enhancing the operation performance of the HMI-HVDC system.

Abstract:The capacitor is one of the most important components in a modular multilevel converter (MMC). Due to the chemical process and the aging effect, the capacitor is subject to deterioration over time which is usually manifested by a drop in capacitance. To identify the abnormal capacitors and enhance the reliability of MMCs, an improved submodule (SM) capacitor condition monitoring method is proposed in this paper. The proposed method estimates the capacitance during each control cycle based on the switching states of SMs, offering advantages such as high accuracy and no adverse influence on the operation of MMCs. Firstly, the aging differences of capacitors in different SMs per arm of MMC are analyzed. Then, the capacitances of SMs that switch on the state are calculated based on the relationship between the capacitor voltage and current during each control cycle. A data processing algorithm is proposed to improve the accuracy of capacitance estimation. Finally, the simulation and the real-time control hardware-in-the loop test results based on real-time digital simulator (RTDS) show the effectiveness of the proposed method.